**Translations of Mathematical Monographs**

1995;
298 pp;
Hardcover

MSC: Primary 82; 47;
Secondary 46; 60

Print ISBN: 978-0-8218-0283-0

Product Code: MMONO/143

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

**Electronic ISBN: 978-1-4704-4560-7
Product Code: MMONO/143.E**

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

# Linear Infinite-Particle Operators

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*V. A. Malyshev; R. A. Minlos*

The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.

#### Readership

Research mathematicians and graduate students working in functional analysis, probability theory, and mathematical physics.

#### Reviews & Endorsements

What distinguishes [the book] from other existing monograph with similar scope … is the emphasis it puts on the contribution of the Moscow school, of which the authors are outstanding representatives. It makes readily available to the mathematical physics community first-hand information on a large piece of relevant work … The elegance and optimal organisation of the exposition in Chapter 3 … is fully rewarding.

-- Mathematical Reviews

The contents of the book comprises the material that has not been treated previously in any monographs and the well-known ones as well … useful for both researchers and graduate students.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Linear Infinite-Particle Operators

- Cover Cover11
- Recent titles i2
- Half title page iii4
- Title page v6
- Contents vii8
- Introduction. What this book is about 110
- Chapter 0. Extended introduction 312
- Chapter 1. Construction of a nonequilibrium dynamics 2736
- Chapter 2. Construction of an equilibrium dynamics 7988
- Chapter 3. Spectral analysis of the Euclidean field transfer matrix 139148
- Chapter 4. Asymptotic completeness for interacting Fermion systems 211220
- Chapter 5. The method of Bethe-Salpeter kernels (Dyson’s equation) 259268
- Guide to the literature 293302
- References 295304
- Recent titles (continued) 299308
- Copy/Reprint page 301310
- Back Cover Back Cover1311